Data structure: \(O = (W, A, Z, Y)\)
Underlying data generating process, \(P_{U,X}\)
## W A Z Y
## Min. :-3.73508 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:-0.64589 1st Qu.:0.6136 1st Qu.:0.0000 1st Qu.:0.0000
## Median : 0.02644 Median :2.0483 Median :0.0000 Median :0.0000
## Mean : 0.01805 Mean :2.1412 Mean :0.4871 Mean :0.4435
## 3rd Qu.: 0.69708 3rd Qu.:3.4273 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. : 3.88609 Max. :5.0000 Max. :1.0000 Max. :1.0000
## Summary of A given W < -1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.493 2.896 2.773 4.225 5.000
## Summary of A given -1 < W <= 0:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.826 2.253 2.275 3.572 5.000
## Summary of A given 0 < W <= 1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.4018 1.8412 1.9875 3.1971 5.0000
## Summary of A given 1 < W:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.367 1.598 2.682 5.000
## CV selected lambda (from one sample): 0.00342499231220454
## The average of CV selected lambdas (from 1000 sample): 0.00387846621405548
## z=1:
## z=0:
## Undersmoothed lambda: 0.000799982807508477
## which is 0.233572146909012 * lambda_CV
## The average of unsersmoothed lambda (from 1000 sample): 0.000851942858017283
## which is 0.217778357408167 * the average of 1000 lambda_CV
## z=1:
## z=0:
## z=1:
## z=0:
## CV selected lambda (from one sample): 0.0016481890921567
## The average of CV selected lambdas (from 1000 sample): 0.00184274700569968
## z=1:
## z=0:
## Undersmoothed lambda: 0.000267629110962862
## which is 0.162377673918872 * lambda_CV
## The average of unsersmoothed lambda (from 1000 sample): 0.000393879557187377
## which is 0.213589118948609 * the average of 1000 lambda_CV
## z=1:
## z=0:
## z=1:
## z=0:
## CV selected lambda (from one sample): 0.00066416866564044
## The average of CV selected lambdas (from 1000 sample): 0.00100946359885929
## z=1:
## z=0:
## Undersmoothed lambda: 0.000320988082768554
## which is 0.483293023857175 * lambda_CV
## The average of unsersmoothed lambda (from 1000 sample): 0.000229565022553988
## which is 0.227979662379109 * the average of 1000 lambda_CV
## z=1:
## z=0:
## z=1:
## z=0: